Universiteit van Amsterdam
Master Thesis
Advanced Matter & Energy Physics
An optical microcavity and
nanoantenna hybrid resonator
Author:
Beniamino Ferrando
Student number: 11798904
Daily Supervisor:
I. M. Palstra MSc
First Examiner:
Prof. Dr. F. Koenderink
Second Examiner:
Dr. S. Rodriguez
April 24, 2020
“To see a world in a grain of sand And a heaven in a wild flower
Hold infinity in the palm of your hand And eternity in an hour”
Contents
1 Introduction 5
2 Background 8
2.1 Local density of optical states . . . 8
2.2 Optical cavities . . . 9
2.3 Plasmonics . . . 10
2.4 Plasmonic antenna - cavity hybrid . . . 12
3 Simulations 14 3.1 Introduction . . . 14
3.2 Realistic models: COMSOL specifications . . . 15
3.2.1 Drude model for permittivity . . . 15
3.2.2 Boundary Conditions . . . 15
3.2.3 Meshing . . . 15
3.2.4 Perfect electric and magnetic conductors . . . 16
3.2.5 Geometric peculiarities . . . 17
3.3 Realistic models: quantitative calculations . . . 18
3.4 Resonance of a nanocube on a mirror . . . 19
3.5 Quasi normal modes of NC on a mirror . . . 21
3.6 The Fabry–P´erot cavity . . . 23
3.7 Putting everything together: the hybrid . . . 27
4 Sample fabrication and preparation 29 4.1 Gold mirrors: physical vapour deposition . . . 29
4.2 Au nanocubes . . . 30
4.3 Spinning dye-doped PMMA thin films . . . 31
4.4 Deposition of nanocubes . . . 32
4.5 O2 descum for PMMA pedestal under the nanocube . . . 33
5 Experiments 34 5.1 Nanocube resonances in dark field microscopy . . . 34
5.2 Confocal fluorescence microscopy . . . 37
5.4 Nanoparticle enhanced Raman of Coumarin 153 . . . 41
6 Conclusion and outlook 44
Abstract:
We have computationally examined the LDOS landscape of a hybrid optical microresonator composed of a Fabry-P´erot cavity and a 75 nm gold nanocube an-tenna. We then develop a wide spectrum of understanding about the individual components: from the nanocube on a mirror scenario to the Fabry-P´erot cav-ity alone. We computationally reach full tunabilcav-ity of the plasmonic resonance and study its induced polarity with quasi-normal modes for the nanocube-on-a-mirror configuration, while for the cavity we create a map of the transmission and reflection spectrum. We finally show asymmetric hybrid resonance lineshapes reminiscent of Fano interference phenomena which exceed LDOS enhancement values for each component when alone by 1/3, at over 15000. We construct a bottom-up assembly method to construct a sample and we then characterize it with dark field microscopy, confocal microscopy, nanoparticle enhanced nonlinear emission and nanoparticle enhanced Raman experiments. We conclude that the Fabry-P´erot-nanocube hybrid resonator holds the potential for monster LDOS en-hancements, with direct implications in the strive for room temperature cavity QED, high fidelty single photon sources for quantum computing and sensor and detector technology.
1
Introduction
Already in classical eras the human race realizes the power of light and its in-credible importance, creating a god to conquer its graces. In classical mythology light is described and conceptualized by means of Apollo. Apollo is a complex character who both represents the sun and heavenly light. He inherits the role from and merges with Helios, the previous generation sun-god. In this ancient conceptualization, it is possible to find the great elusiveness of light portrayed as both the source of power and the beam connecting the earth to the heavens. In a way, Apollo is the eye of the gods: he illuminates the earth with energy and under the same light collects information on humans, whom he interacts with and at times punishes.
Light is unique and, as we find in Greek mythology, has always been a thought provoking phenomenon for the human kind. As we now know, light travels in vacuum at a formidable speed rendering it impossible for the human to experience. To study light effectively it is made to interact with matter or with itself in a nonlinear medium and in some high energy physics processes. In the last century and a half, we have reached an unprecedented level of formal understanding of the existence of light-matter states where their individual properties fuse creating a mixed state. A commonly used tactic to study light-matter interactions is by the use of optical cavities. Optical cavities have the ability to trap light for long periods of time with remarkably narrow bandwidths. Perhaps the simplest optical cavity is the Fabry-P´erot cavity [53], which confines light between two planar metallic mirrors to create a set of standing waves of well-defined frequency and wavelength between them. Over the past years, this concept has been greatly expanded upon, and a wide variety of optical cavities has been developed. To name a few examples, microdisk resonators [63, 48], and microspheres [62, 67] function as a sort of racetrack for light. Through total internal reflection, the light can’t radiate out of the structure, and therefore runs in circuits around the edges. Micropillar cavities [58, 37], and photonic crystal cavities [70, 57, 27], both use a patterned section of material to create a frequency range where light can’t propagate, known as a photonic band gap. When designed carefully, these can be used to create mirrors of extremely high reflectivity, and light can be trapped
between them much in the same way as the two mirrors of the Fabry-P´erot cavity. Many of these cavities can be coupled to a light-emitting systems [36, 32, 63, 58, 61]. In these studies, the cavity alters the photonic environment of the emitter, altering its behavior. As we will discuss later in this work, the main benefit of optical cavities (in the context of this work) is their ability to retain light for long periods of time, and optimization of this property is of ongoing interest for many of the aforementioned systems.
Antennas are metallic structures that can be used to capture light and con-versely steer radiation. At the macroscale, antennas have been in use for over a century to send and receive radio waves. More recently, they have been shrunk to the nanoscale in order for them to be resonant with light at optical frequencies. They are of particular interest for coupling with emitters, as they can steer the emitted light in a desired direction. Like optical cavities, antennas range widely in complexity. From systems as simple as a single rod to compound systems like the Yagi-Uda antenna [44] or antenna arrays [16], dimer systems [8, 29, 39], and slot antennas [30]. Systems where an antenna is placed close to a metallic plane are widely studied for their high field enhancements and strong interactions with emitters in the gap [1, 14, 60, 7, 6, 66]. For an overview of these topics, see the following reviews[49, 64]. For antennas, the main property of interest is their abil-ity to not only steer light, but also confine it in volumes much smaller than the wavelength cubed.
In this work, we will focus on the combination of an optical cavity with an antenna. The idea to combine these two has been of increasing interest in the past years [23, 19, 15, 31, 17, 47] in order to further manipulate the emitters behavior, and improve, among other things, the speed of operation and the directivity of the emission. We will discuss how the combination of both systems allows one to benefit from the strengths of both components.
Looking at light and matter interacting with one another at the nanoscale fea-tures in the geometry and nature of space change the electromagnetic environment giving rise to fascinating phenomena. We investigate a hybrid Fabry-P´erot cavity and a plasmonic nanoantenna system. We study its potential in enhancing the radiation of an emitter placed close to the nanoantenna, by increasing the density of states available at that position in space and we hypothesize that the hybrid resonator has higher LDOS enhancement when compared to its single components.
We investigate resonances of a nanocube on a mirror as a function of antenna dis-tance from the mirror aiming to reach full tunability of the plasmonic resonance, and we hypothesize that the further away from the mirror the antenna the more in the blue part of the spectrum the resonance should be. In the strive for a probing mechanism for the local density of optical states, the enhancement of pho-toluminescence of organic dye molecules is investigated in relation to a resonating nanocube on a mirror configuration. We hypothesize that either photolumines-cence absolute counts or photoluminesphotolumines-cence lifetime can yield the conclusions we search for. In studying the nanocube’s pump enhancement potential we look at nonlinear emission and absorption processes expecting to observe increased pho-toluminescence at the cube’s location. Furthermore, we probe the tight focusing of the field in the near field of the nanocube by studying the Raman signature of molecules segregated to the nanogap between nanocube and mirror. We thus aim to construct a full and comprehensive understanding, both computationally and experimentally, of the nanocube on a mirror scenario in view of Fabry-P`erot and nanocube experiments.
The broader scope of this research is enhancing the weak interaction of light and matter. This is an important endeavour with many applications ranging from detector to quantum computing technology. Transistors in computer chips have been reducing in size year after year calling for miniaturization of light sources and detectors in the strive for novel electro-optic integrated circuits. Hybrid res-onators and their promising properties have conquered themselves a seat in the spotlight as candidates for many nanoscopic light manipulation applications. In this thesis section 2 explains briefly the most important physical concepts relevant to the work. We then present the results of our simulations in section 3; section 4 is devoted to experimental method and detail while section 5 presents and dis-cusses experimental results. Section 6 concludes this work and describes important outlook of the research.
2
Background
This section draws a sketch of the basic concepts operating behind the simula-tions and proposed experiment. We will briefly introduce local density of optical states, optical cavities, plasmonics and will conclude by introducing cavity-antenna hybrids.
2.1
Local density of optical states
The density of states describes the number of states that can be occupied by a system per unit of frequency. LDOS refers to the density of states available at a specific region of space compared to an arbitrary reference [52].
An intuitive picture of LDOS enhancement can be constructed by imagining a spontaneous emission process as a random walk taken by the emitter where, for each time interval δt, the random walker takes a step over a fictitious 2D lattice, with the direction of each step being uniformly distributed between all possible choices. The emitter does not emit at each step, but only when it finds a door. Lets then also say that for each step it has an isotropic probability P of finding the metaphoric door to emit through, thus signifying some emission for that step. If the environment provides an LDOS enhancement, the probability for the random walker to find a door is now Z where P <Z. We thus have a way of enhancing spontaneous emission by cleverly designing the environment around the emitter. This is also known as the Purcell effect, when the enviornment (generally an optical cavity mode) is coupled with an emitter [52]. This is described by the Purcell factor which scales with quality factor (Q) and one over mode volume (V).
FP = 3 4π2 λ n 3Q V , (1)
where n is refractive index, lambda is the wavelength, Q refers to the number of cycles within the resonator before the light is lost, V is the volume of the electromagnetic mode [55].
In the LDOS calculations for a specific resonator presented in this work, we normalize the radiated power from the antenna on a mirror to that of an ideal dipole in the same medium. We thus get a number for the radiative enhancement of the dipole thanks to the the photonic environment the dipole is in. Previous
works have identified LDOS enhancements near planar interfaces, in planar cav-ities, in microcavcav-ities, at plasmonic antennas, as well as in coupled resonances of plasmonic and photonic constiuents. For instance, reference [21] has identified LDOS enhancements by part of hybrid photonic resonators up to a factor 8 times higher LDOS than the single cavity and a factor 3 higher than the antenna alone.
2.2
Optical cavities
Optical cavities are devices that use reflection of electromagnetic (EM) waves to trap light. These waves form a standing wave within the cavity creating an optical resonator, not too different from a string on a musical instrument.
The cavity that is the key player in this thesis is composed of two parallel planar gold mirrors. These form a spacing between each other which places well defined boundary conditions on the electromagnetic field in that region of space. For this reason the solution to the wave equation isn’t a plane wave as in free space but a set of standing waves whose frequency depends on cavity spacing (or mirror separation). The portion of a plane wave that passes through the first mirror will have some portion of it reflected off the second mirror. It will then interfere with itself, forming a standing wave. In figure 1 a first and tenth order mode are sketched. In an ideal case, the equation for the resonant condition of such an etalon reads:
λ = 2L q ,
where λ is the resonant wavelength in vacuum (n here was set to 1), L is the optical path length between the two mirrors, q is an integer called the axial mode order and describes the number of intensity maxima within the resonator. The etalon will have a sequence of resonance wavelengths separated by:
∆λ = 2L in vacuum [35].
This is very similar (if not analogous) to propagating waves in a taut wire fixed at its two ends. Just like in the example of the wire, the electromagnetic field should be stationary, or zero, at the interfaces with the mirrors. It is intuitive
Figure 1: Field distributions within the resonator for an integral multiple q of half the wavelength. Interference effects yield standing waves [35].
that in this scenario the electromagnetic field strength is enhanced within the cavity, away from nodes of the field. The duration for which light is trapped in the cavity is linked to the quality of the mirrors and medium. Optical cavities typically have low losses, allowing the light to resonate for a long time before it is lost. This affords them a high Q [65].
2.3
Plasmonics
Cavities are bound by interference effects, which limit the mode volume to ∼ λ3. The longer light is stored within the cavity the higher Q factor of the cavity [52]. Altered photonic environments of this kind have been largely exploited to reach high LDOS enhancements. Cavities of this configuration operating at optical frequencies typically have large mode volumes [22]. Given that the Purcell factor scales with QV it is vital to reduce the mode volume as much as possible. For this
reason we consider plasmonic resonances, which have been reported to result in ultrasmall mode volumes [28]. Incident light on a metallic nanoparticle can induce
Figure 2: Interference of locally excited surface plasmons in a silver film. By interference, surface plasmon standing waves can appear [35].
oscillations in its free electron plasma [4]. In figure 2 these can be seen on a thin silver sheet. These are confined in frequency space by the geometric boundary conditions of the particle: size and shape. These oscillations are called localized surface plasmon and have a preference to oscillate at a specific frequency due to the size and shape of the particle. This phenomenon is the localized surface plasmon resonance (LSPR). This sloshing of the electrons back and forth interacts with the EM environment, fundamentally changing the extinction cross section of the particle which is the nanoscopic equivalent of the shadow of a macroscopic object. These LSPR’s allow for a high level of interaction between the antenna and the photonic environment [41]. This is expressed, among other things, by a large scattering and extinction cross section. Plasmonic antennas on resonance with an incoming light beam can cast a shadow over 10 times its own surface area. To put this into comparison, it would be as if a human being casts a shadow the size of a London double-decker bus. In addition to this, plasmonic antennas offer another benefit. Their metallic properties allow for highly sub-diffraction limited focusing of light, which makes makes sub-wavelength mode volumes possible, for example in the gaps between two metallic particles. Nanospheres have been shown to reach ≈ 22 LDOS enhancements [3] [45], nanorods ≈ 9 [71] [40], bow ties ≈ 800 [42],
Figure 3: Sideview sketch of hybrid planar mirror optical cavity with nanocube on the lower mirror. The red dot is at the point dipole position. Not to scale.
nanopatch antennas ≈ 2000 [2] [34]. Small V comes at a cost, namely that the LSPRs are lossy oscillations because of heat generation by the electronic plasma. Typical Q factors for plasmonic nanoantennas are Q <50 [56][28]. They however seem a great candidate to overcome the main limitation of cavities, large mode volumes.
2.4
Plasmonic antenna - cavity hybrid
In this thesis we study hybrid plasmonic resonators. A hybrid photonic-plasmonic resonator is built from an optical cavity that works by interference, and a plasmon nano-antenna placed within it. In figure 3, a sketch of the system we propose can be found. It is called ”hybrid” because the two resonances hybridize. Hybrids have been proposed and shown as a tool to combine the best of both the nanoantenna and cavity systems [68]. The proposed plasmonic nanoantenna-cavity hybrid system we study, a planar Fabry-P`erot and a plasmonic gold nanocube an-tenna, has the potential to demonstrate strong emission enhancements that surpass the antenna or the cavity as independent components. High Q cavities and low mode volume antennas are indeed promising candidates in the search for high LDOS enhancements. In order to couple an emitter to an antenna the coupling strength between the two has to exceed the loss rate of the nanoparticle. This is a strong limitation as nanoantennas on the one hand are lossy oscillators. On the other, antennas can be designed to have directional radiation patterns which can greatly improve the coupling [2]. Recent studies have shown that in some
cases the inclusion of a nanoparticle to a cavity can increase the LDOS [21], while a different study has shown that the nanoparticle-cavity ensemble showed a sup-pression in LDOS [26]. When a broadband resonator and a narrowband resonator (e.g. antennas and optical cavities respectively) interact, Fano lineshapes arise in their combined response. In the case of optical hybrid systems, this lineshape appears in the LDOS as a function of frequency. It is interesting to mention that Fano lineshapes, the general interaction between any broadband and narrowband resonance, appear in a number of different physical systems with examples ranging from hydrodynamics [10] to atomic physics [24].
In this research the antenna configuration we chose is the nanocube on a mirror configuration which has been proven to reach high LDOS enhancements and a high directivity of the field [2]. This system is further suitable for this investigation due to its cheap and bottom-up assembly. Finally, its simplicity allows us to inves-tigate the planar cavity and the nanoparticle on mirror (NPOM) configurations independently before studying the hybrid system where the two systems share the lower mirror.
3
Simulations
3.1
Introduction
In order to simulate the system we use COMSOL Multiphysics which we set up to be as realistic as possible. The antenna is placed on a planar metallic (gold) mirror and a second gold mirror parallel to the first is placed leaving some empty space (of refractive index n = 1) between the two mirrors which forms the effective cavity. A picture of the geometry is shown in figure 4. In order to save on computational power the symmetries of the system were exploited. In this way just one quarter of the system has to be meshed and computed. Highlighted in blue are the two planar gold mirrors 40 nm thick and the gold 75 nm nanocube. The gold mirrors are both on glass substrates which are the other layers in the figure. Notice a 15 nm n = 1.4 spacer layer between the cube and the bottom mirror.
3.2
Realistic models: COMSOL specifications
3.2.1 Drude model for permittivity
For gold and silver we used the Drude permittivity, of the form:
Au(ω) = 1 −
ω2 p
ω2+ iωΓ
with: ωpAu = 2π·2.068e15 Hz, ωpAg = 2π· 2.3e15 Hz, ΓAu = 2π· 4.449e12 Hz, ΓAg
= 2π· 5.513e12 Hz [9]. The permeability is set to 1. For glass we use n = 1.52, for the spacer film and protective shell of the cube we use n = 1.4.
3.2.2 Boundary Conditions
In LDOS calculations and in transmission calculations we have scattering bound-ary conditions that encapsulate the geometry of the system. This ensures that there are no artificial reflections of waves at the limits of the geometry, rendering them effectively transparent to the electromagnetic waves at normal incidence. In calculating quasi normal modes, we utilize perfectly matched layers (PMLs) as boundary conditions. These serve a similar function to the scattering boundary conditions but are most suited in this case. PMLs are sizeable extra domains added around the system we’re simulating to ensure that all fields can decay from the system without unwanted reflections and effects. Being COMSOL a finite el-ement solver, it requires a mesh, or a numeric discretization of space to solve over our structures. This must be carefully matched between PMLs and our actual structure to avoid artificial reflections at the interface.
3.2.3 Meshing
The meshing, visible in figures 5 and 6, was automatically generated by COMSOL. Meshing creates a numerical discretization covering the entire system. In this way it is possible to control the amount of points solved for per unit of space. The preferred meshing for finite element solvers is tetrahedral mesh, given its flexibility to fit complex geometries. In figure 6 the nanocube is zoomed in. We are most interested in the field surrounding the cube and we thus have finely meshed the surrounding region compared to the rest of the system. Mesh was generated with calibration for general physics, maximum element size 0.0865 µm, minimum size
0.0156 µm and maximum growth rate at 1.5. The free tetrahedral generator was then set to generate four mesh sizes for the nanocube shell and cube, spacer film, gold mirror and vacuum. In the element size parameter it is possible to define maximum element size. We defined three values: fine mesh, middle mesh and coarse mesh, as follows: 10−8 m, 3.34 ∗ 10−8 m, 7.142 ∗ 10−8 m.
Figure 5: Tetrahedral meshing in our sys-tem.
Figure 6: Zoom in on the mesh surround-ing the nanocube.
Figure 7: COMSOL mesh element qual-ity statistics.
COMSOL proposes a mesh quality statistics function able to yield qualitative information about the mesh quality. This is reported, for the mesh used in our models, in figure 7.
3.2.4 Perfect electric and magnetic conductors
Perfect electric conductor (PEC) and perfect magnetic conductor (PMC) are two tools in COMSOL which are required when looking at symmetric cuts of a system, in presence of a dipole. Given the orientation of the dipole in the z-direction, normal to the lower mirror, we set up a PEC and PMC pair as follows:
(a) PEC (b) PMC
Figure 8: PEC and PMC pair as set up for all LDOS calculations.
3.2.5 Geometric peculiarities
The cube edges have been rounded with a rounding radius of 8 nm. The curvature is visible in figure 9. In order to greatly improve the mesh element quality, a 3 nm pedestal is created under the cube, extended from the existing shell surrounding it. This entails squaring off the edges of the shell where it is in contact with the substrate. The main reason for the great improvement in mesh quality is because the tetrahedral mesh struggles to cover the interface between cube and substrate when very thin asymptote-like curves form. These features if not carefully meshed can cause problems in performing calculations. The pedestal is visible in figure 9.
(a) (b)
Figure 9: Enlargement of the nanocube geometry for the simulated nanocube. The dipole is placed within the pedestal visible in figure 9, at coordinates in
nanometers: (0, 42,-3). This is implemented as a ”free” point at the user defined coordinates, which is then, in the electromagnetic waves module, defined as point dipole with dipole moment d = 5 ∗ 10−12 A*m, in orientation z.
3.3
Realistic models: quantitative calculations
In the endeavour of simulating cavity - antenna hybrid systems we first look for the plasmonic resonance of a single gold or silver 75 nm nanocube on a metallic mirror. We set the top mirror of the cavity and its holder to vacuum, in our model. The nanocube has a 3 nm PVP shell surrounding it to protect it from degrading through oxidation. We add a thin film (spacer layer) on the mirror below the cube and firstly study the effect of its thickness on the nanocube resonance. We place an ideal dipole under the cube and within the film, under a corner of the nanocube. This has been shown to have the highest LDOS [2]. We calculate radiated power from the dipole in the system. Radiated power is calculated by COMSOL by integrating the Poynting vector through a closed surface. This is a rectangular surface constructed around the nanocube and dipole. To calculate LDOS one strictly needs a closed surface that encloses the source but not any absorbing object. Since in this work we are mainly interested in the radiative part of the LDOS, we instead choose an oblong surface that contains both the dipole and the nanocube. This means we report the LDOS from which the absorption due to the cube is subtracted. By performing such a calculation COMSOL is able to yield a value for radiated power from the dipole-cube-mirror ensemble. We normalize that power by the radiated power from an ideal dipole in a medium of the same refractive index as the COMSOL dipole, which is specified by Larmor’s equation. By this token we are able to quantify the LDOS enhancement of the photonic environment we place the dipole in. Larmor’s equation reads:
P = |µ|
2
4π0
n3ω4 3c3 .
where |µ| is the dipole moment, n is the refractive index, ω is the 2π times the frequency of oscillation of the dipole, is the permittivity of the material, 0 is the
3.4
Resonance of a nanocube on a mirror
To investigate our nanoparticle on mirror configuration we systematically vary the spacer thickness under the cube and calculate LDOS of an emitter in the gap, for a gold and silver nanocube. The result we present in figure 10a shows Lorentzian line shapes in LDOS. From our calculation it appears that gold has plasmonic resonances further in the red compared to silver for two otherwise geometrically identical nanocubes, both over a gold mirror. The driving source within the simu-lation is an ideal dipole in the nano-gap oriented normal to the mirror (z-direction). We find that the thickness of the spacer layer between the cube and the mirror strongly affects the spectral position of the LDOS peak. LDOS strongly increases with narrower gaps. Approaching the cube to the mirror, done here by reducing the spacer thickness, the resonance shifts towards the red part of the spectrum and conversely when the cube is distanced further from the mirror the resonance blue-shifts. Finally we find that with decreasing spacer thickness LDOS enhance-ment increases, likely due to the tight focusing of the field in the nano-gap. We report the highest LDOS enhancement value of 22500 with spacer thickness 10 nm for a gold nanocube.
(a) (b)
Figure 10: (a) Plasmonic resonance with respect to film thickness for silver and gold 75nm nanocubes. (b) Resonance peak in wavelength per metal and spacer thickness.
From figure 10a, we calculate the Q factor for the nanocube. By taking the width (in frequency) at FWHM and dividing it by the resonant frequency we find Q for the Au nanocube on a 15 nm spacer to be 9.81. More formally: Q = F W HMω
In figure 10b the LDOS resonance peak is in frequency per each spacer thickness, for gold and silver nanocubes. It is possible to say that in our model gold cubes yield higher LDOS values with redder resonances. This could be due to matching metals between cube and mirror, which would result in matching impedance.
3.5
Quasi normal modes of NC on a mirror
With a quasi normal mode (QNM) solver provided by Kevin Cogne`e we attempt to solve for the (quasi)-eigenmodes of the nanocube-on-substrate system [46]. In this way we are able to characterize the nature of the nanocube modes and thus form an idea of the near field of the cube [69]. Reported in figure 11 is the solution we find for a gold 75 nm nanocube on a 15 nm spacer on a gold mirror. We are confident we are investigating the same mode given the good match in resonant frequency and Q we find from the LDOS and QNM models. The green arrows represent the direction of the field at that point in space, the underlying colour map is the amplitude of the electric field, normalized by the quasi normal mode factor.
Figure 11: QNM of nanocube on a mirror with 15 nm spacer. Resonance at 5.45E14 Hz. Green arrows represent field direction while surface is amplitude of electric field.
From the eigenvalue solution we selected we can calculate the Q for this mode:
Q = Re(ω) 2 ∗ Im(ω) =
ω0
2γ (3)
By using the real and imaginary part of the eigenvalue, as done in the work by X.Zheng [72], we get Q = 9.72. Observing figure 11, we can infer from the field direction that we are looking at a vertical dipole and a horizontal dipole or a higher order mode. The frequency of the mode is in accordance to our previous simulations for the same geometry, with a minimal discrepancy of 0.7E14 Hz. We are confident we are investigating the same mode given the good match in resonant frequency and Q we compute from the two models.
3.6
The Fabry–P´
erot cavity
By turning the nanocube within the cavity to vacuum in our COMSOL model, we study the empty cavity configuration. By driving the system with a plane wave we calculate transmission and reflection through the cavity. The transmission peaks and reflection dips in figure 12 show the resonance condition for the cavity.
Figure 12: Transmission and reflection through the cavity in absence of the nanocube for the relevant cavity openings.
Figure 12 shows the resonance conditions for cavity openings from 450 nm to 650 nm. As expected the transmission of the cavity off resonance is near zero while reflection is near one. Our model was not able to compute transmission and reflection in presence of the nanocube. The model returns errors we were entirely unable to resolve when computing transmission and reflection in presence of the nanocube. Cavity resonances appear at redder positions in frequency with respect to calculated peaks considering ideal mirrors. We use the following equation to
estimate the resonance wavelengths of an ideal etalon: λr = 2∗cavityn , where λr is
the resonant wavelength, n the mode order index and cavity is the cavity opening in nanometers. We are looking at the second order (n = 2) mode of the cavity. The difference between the calculated resonances varies with cavity opening as in figure 13. The discrepancy is 0.4E14 Hz for the reddest cavity opening at 650 nm while it reaches 0.84E14 Hz for 450 nm cavity opening. We know from reference [5] that metallic mirrors don’t reflect EM waves at all frequencies in the same way: the reflection coefficent is complex and depends both on ω and in plane wave vector kk. The increasing discrepancy between the model and the ideal etalon could be
pointing at the degrading reflectivity of the mirror with frequency since we are at normal incidence on a planar pair of mirrors. We attribute the peak height variation to the coarse sampling in frequency we were forced to choose in order to maintain a reasonable computation time interval. It is the case that for each transmission peak we do not have a satisfying number of data points.
Figure 13: Resonant wavelength per cavity opening computed by our model and computed for an ideal Fabry-P´erot, for the second order mode.
is not π as ideal reflectors would. Metal losses are also not taken into account in our ideal etalon equation. We hypothesize that these could be the principal reasons behind the discrepancy between the ideal cavity resonances and the computed ones. This is entirely calculable by numerous methods, such as the transfer matrix method. Due to time constraints this could not be carried out.
Following the work of H.Doeleman [21] we investigate the LDOS landscape for the bare cavity as a function of frequency for a range of cavity openings. We drive the cavity with a dipole oriented normal and parallel to the mirror. LDOS is then quantified at the same location as the driving dipole in the antenna system. The results are reported in figures 14a, 14b respectively.
(a) (b)
Figure 14: LDOS in the region under the nanocube in absence of the nanocube. In figure 14a the dipole is oriented normal to the mirror while in figure 14b the dipole is oriented parallel to it.
The graphs in figures 14a, 14b do not show any signature of the resonances that are evident in normal incidence transmission. In fact, figures 14a, 14b show a near flat LDOS in frequency for both a vertical (normal to the mirror) and horizontal dipole. This is due to the fact that planar microcavities, unlike e.g. whispering gallery mode cavities, do not have a discrete spectrum of high Q modes. Instead, the high Q mode evident under normal incidence continuously shifts to higher frequency with increasing off-normal incidence angle. Since the dipole is a point source it can couple to modes at all parallel momenta. The normal incidence resonance does not stand out. As formally argued on page 39 of [5], another reason why LDOS doesn’t show peaks is because of it being calculated close to the metallic mirror. The radiation pattern of the dipole within the cavity is influenced
by the orientation of the driving dipole. LDOS is the sum of the radiated power over three possible orientations, in our case this is strongly altered by the close proximity of the mirror to the dipole. Indeed, for this dipole position the LDOS is essentially identical to that for a dipole above a single mirror.
3.7
Putting everything together: the hybrid
In this section we combine all components of the model at once, thus creating the final model which is composed of the Fabry-P´erot cavity and the nanocube antenna on a mirror. We calculate the LDOS enhancement in the nanogap below the cube in the same way we did for individual components.
Figure 15: The grey vertical lines rep-resent the transmission resonance fre-quencies calculated from the transmis-sion model.
Figure 16: The grey vertical lines rep-resent the transmission resonance fre-quencies calculated from the transmis-sion model.
Figure 17: The grey vertical lines rep-resent the transmission resonance fre-quencies calculated from the transmis-sion model.
Figures 15, 16, 17 represent three different sets of cavity resonances. In these three cases, we calculate the LDOS when the cavity resonance is red detuned, less red detuned and blue detuned with respect to the antenna, respectively. The film
thickness in this case is kept constant at 15nm. Because of a discrepancy in calcu-lated and simucalcu-lated cavity resonances the resonances have red shifted significantly with respect to the originally decided values. For the three combinations we see an LDOS lineshape arising from the interaction between the plasmonic resonance and the cavity resonances. In the red detuned case we report an LDOS enhance-ment value of 8143 (with 610 nm cavity spacing), for the less red detuned case, 8003 (cavity at 550 nm) and finally for the blue detuned case 15983 (cavity at 490 nm). We clearly find greater enhancement for a blue detuned cavity with respect to the antenna, since the LDOS enhancement nearly doubles when considering the just-under 8000 LDOS enhancement of just the antenna on the mirror. An-other feature of the hybrid lineshape is that this resembles the asymmetric Fano interference signature.
Previous work has shown that the highest LDOS enhancement is achieved with the cavity resonance red detuned with respect to the plasmon peak [20]. In our scenario it seems to be diametrically opposite: the highest LDOS value is achieved with the cavity resonance on the blue shoulder of the plasmonic peak. While one of the many differences between the two experiments lie with the nature of the cavity, one supporting single whispering gallery modes the other supporting a su-perposition of modes, formally looking at the difference between the two scenarios might yield important insights in the search of the perfect photonic cavity-antenna hybrid.
4
Sample fabrication and preparation
Making the mirrors with cavity experiments in mind we strived to strike a balance between transmissivity and reflectivity of the mirror. Following additional simu-lations, we decided that 40 nm thick gold mirrors would be successful in achieving the required specifications. Glass 24 mm x 24 mm VWR microscope coverslips were piranha cleaned using base piranha for 10 minutes, rinsed with IPA and blow dried in the cleanroom in preparation of metal deposition.
4.1
Gold mirrors: physical vapour deposition
To fabricate the mirrors an electron beam physical vapor deposition (EBPVD) was used. The device employed is the Polyteknik Flextura M508 E. The machine has 8 rotatable crucibles which hold the evaporation material. The gold crucible is heated and its contents evaporated by means of an electron beam (E-beam) at 10 kV 0.5 A in energy. The device operates under high vacuum ensuring that the vapour impinging the sample is almost entirely the desired material, in our case, gold. The sample size can’t exceed 10 cm in width and 4 mm in thickness. In order to monitor the evaporated thickness the thickness of the anode layer is monitored by two quartz thickness monitor crystals. The mass increase per unit area over the crystals is quantified by measuring the change in resonant frequency of a quartz crystal resonator. We followed a recipe to evaporate gold, at a low rate in order to increase the sensitivity of the evaporation, which is reported in table 1. A base pressure at the process chamber of at least 10−7 mBar has to be reached in order to ensure successful deposition. This can be a lengthy process and depends on servicing standards and prior usage of the device.
Time/ Thickness Rate Emission current Substrate shutter Base Pressure 300 s - 0-40mA (ramp) Closed 10−7 mBar
180 s - 40mA Closed 10−7 mBar
15 nm 0.1 nm/s 0mA Closed 10−7 mBar
40 nm 0.1 nm/s 25mA Open 10−7 mBar
120 s - 25-0mA
(ramp)
Closed 10−7 mBar
300 s - 0mA Closed 10−7 mBar
Table 1: EBPVD recipe used to fabricate 40 nm gold films. Ramp steps are included for smooth increasing and reducing of emission current. Sudden jumps in current can damage the device.
4.2
Au nanocubes
The cubic gold nanoparticles used were provided by Eitan Oksenberg from AMOLF, manufactured by Nanopartz. The stock concentration of the nanocubes is charac-terized with their optical filtering properties: OD1. These are monocrystalline Au 80 nm nanocubes encapsulated in a protetive shell of approximately 3 nm thick Polyvinylpyrrolidone (PVP). In figure 18a a transmission electron microscope im-age of a nanocube is reported. In figure 18b, an imim-age taken with the scanning electron microscope is reported, the protective shell surrounding the gold nanocube can be clearly identified. This image was captured after the electron beam was focused at high magnification on the nanocube for tens of seconds thus heating the nanoparticle up. It is likely that upon heating the PVP expands, making it appear larger.
(a) TEM image of 80 nm Au nanocube.
(b) High magnification SEM image of 80 nm Au nanocube with inflated shell.
Figure 18: Transmission and scanning electron microscopy images of 80 nm Au nanocubes.
4.3
Spinning dye-doped PMMA thin films
To create thin spacer films over the gold mirror we select Poly(methyl methacry-late) (PMMA 950k) given its availability and accessibility as the polymer matrix. In our investigation of LDOS enhancements, we select fluorescent molecules as probing mechanism. Many works in the field have compared properties of emitters as fluorescent labels [59] [25]. Coumarin 153 is a fluorescent organic dye molecule of molecular weight 309.28 g/mol which is soluble in ethanol and anisole. Its emission peak is at 530 nm and its absorption maximum is at 423 nm in ethanol [11]. It was provided by us by the EUV Plasma Processes group. It was chosen as the molecule of choice due to its immediate availability and good alignment between emission peak and nanocube resonance and pump absorption maximum. The available optical pump was a blue 450 nm pulsed PicoQuant LDH-P-450B.
In order to consistently spin thin films of desired thickness we check the thick-ness of the film with a profilometer as a function of two parameters: dilution factor and spinning speed. The profilometer is a KLA-Tencor P-7. This is a mechanical, stylus-based step profiler with sub-angstrom resolution available in the clean room laboratory. We change the concentration of PMMA to Anisole and measure the thickness in one case in the other the revolution speed and then measure thick-ness. The sample is manually scratched with a vertically held tweezer and then the scratch is placed under the center of the profilometer which drags its stylus
over the scratch.
The aim of this procedure is to create a recipe to spin thin PMMA films that can be used as spacers and as medium for fluorescent molecules. Qualitatively, most ethanol soluble fluorescent dyes will not affect overall film thickness.
(a) Dilution factor vs thickness of film. (b) RPM vs thickness of film.
Figure 19: Film thickness versus different parameters.
Figure 19a was generated maintaining spin parameters as: 4500 RPM, 2000 acceleration in steps of 45 s. For figure 19b the dilution factor used was 2. We spin PMMA from anisole in a 2 weight percent (2wt%) solution. This is obtained by taking 4 mL of an 8wt% PMMA 950 in anisole solution and adding 12 mL of anisole. We then spin this solution at 4500 rpm, 2000 rpm s−1 for 45 s to achieve a uniform film of 20 nm or below. We qualitatively investigated whether the drop volume plays a role in the film thickness: at very low drop volumes (≈ 10 µL ) uniformity issues arise but film thickness is otherwise unaffected by drop volume. With such thin films it is not necessary to post-bake the PMMA as is common in other recipes.
4.4
Deposition of nanocubes
We dropcast 90 µL of diluted nanocube solution. We find that at this volume most nanocube concentrations will form clusters of nanocubes and finding isolated nanoparticles becomes challenging. In order to resolve this issue we dropcast on the spincoater with the following parameters: spin at 500 rpm, 200 rpm s−1 for 15 s. Most concentrations will yield isolated nanoparticles. This was tested on
substrates from 12x12 mm in size to 24x24 mm om size, and surfaces that include glass, silicon, gold and PMMA covered gold and silver.
4.5
O
2descum for PMMA pedestal under the nanocube
The overall aim of this part is to achieve better contrast from background PL of the film, since the difference in PL between the molecules under the nanocube and the ones within the rest of the film is small. To find the nanoparticles on our substrate and probe the LDOS below them we spin a fluorescent PMMA layer on the mirror. We then deposit the cubes on this layer. We then create pedestal below them with oxygen plasma. The aim of this procedure is to get rid of the PMMA film that is not protected by the nanocubes. In this way the only photoluminescent (PL) part of the thin film is the portion under the nanocube. This is the region of interest in the strive to probe LDOS enhancements by our configuration.
In order to achieve this, we used a oxygen plasma PMMA etching recipe named PMMA etch with the Plasmalab 80+, Oxford Instruments. This recipe is a tai-lored oxygen plasma descumming recipe. Recipes are available on the Plasma-80 software, made available by the cleanroom staff.
The radio frequency generator was turned on by means of a switch on the front panel of the device. The etch time was set to 10 seconds. The inductively coupled plasma (ICP) parameter was set to 0 W. Forward power (FWD) was set to 100 W. ICP is related to the isotropicity of the etch, which in our case we want to minimize in order to avoid etching the film below the nanocube.
5
Experiments
5.1
Nanocube resonances in dark field microscopy
In this section we measured the scattering spectrum of nanocubes on a metallic mirror illuminated through a dark field microscope. A schematic of the microscope can be found in figure 20. The white light source is a 100W tungsten halogen lamp by Philips with range 360-2600nm, mounted in a Nikon lamphousing, (1) in schematic. (2) is a fieldstop, (3) an aperture stop, (4) a reflected light dark field block, (5) 50x 0.8 NA Nikon MUE41500 dark field objective, (6) sample mount, (7) tube lens, (8) is a 70/30 Thorlabs BS022 beamsplitter, (9) an Avantes Avaspec 2048TEC-2-USB2 with 600 lines/mm gratings, (10) mirror and (11) a CMOS colour camera of Imaging Source (DFK 21AU04) [50].
Figure 20: A schematic of the Cicero dark field microscope setup made by Janika Dominique van Moergestel BSc in 2013 [50].
In these measurements the nanocubes are directly dropcasted on the mirror, without a PMMA spacer. The spectra are the scattered light off a suspected single cube. The microscope in question is reversed upside down, with the objectives pointing up from the ground. We investigate the resonance conditions of the nanocubes.
Finding nanocubes is made easier by the fact that when dropcasted they appear as colorful, doughnut-like ring shapes on the camera. In figure 21b these are visible. Such doughnuts have been previously reported in the context of nanocubes on a mirror configuration [13]. These shapes in their far field radiation pattern could to some extent be linked back to the near field dipole structure of the nanocube on a mirror configuration. In solving QNMs for nanocube on a substrate we have found that the structure of the induced polarity in the cube is ruled by a superposition of a dipole and quadrupole or multipole. This can’t entirely be reconciled with the doughnut shape we report which could presuppose a vertical dipole induced in the nanocube. As found in this recent work for a spherical gold nanoparticle on a mirror, different gap modes result in radically different field distributions, some with nodes at the geometric center of the particle [43]. Nanocubes are further recognizable by the colour they scatter on the camera. While this may change with camera settings, they still appear a distinct color when compared to dirt particles on the camera. We report a non-scientific result in figure 22 that shows the beautiful colors 80 nm nanocubes scatter. This can be used qualitatively to find or distinguish single nanocubes on a substrate.
(a)
(b)
Figure 21: (a) dark field spectra of 5 different nanocubes on a gold mirror. (b) image of nanocubes on the mirror taken with CMOS colour camera of Imaging Source (DFK 21AU04), taken with objective Nikon 100x 0.9NA (LU Plan Apo).
We measure the scattering spectrum of 80 nm Au nanocubes on a Au mirror. The integration time on the Avantes Avaspec spectrometer was 1 second. Scattered light is collected by aligning a multimode fiber with light coming from the main
axis. This is done by illuminating the camera with a fiber by coupling a light source to the fiber. In this was a bright dot is produced on the screen. A marker is then placed, on the computer screen, where the bright spot appears. To then capture spectra one end of the fiber is swapped from the light source to the spectrometer. Nanocubes are aligned under the marker on the screen and a spectrum is recorded, making sure the microscope is in focus on the substrate.
These measurements show peaks at 600 nm. The spread in intensities of each scattering spectrum is linked to the observation that not all cubes are equally bright, however the FWHM is also almost constant over all 5 nanocubes. For each measurement of a doughnut feature on the camera, a background spectrum was taken in the vicinity of the pertinent nanocube and subtracted from the spectrum. Dark counts were recorded at the beginning of the measurement procedure, with the laboratory TL lights off, and consistently subtracted from each spectrum. Each spectrum was recorded with TL lights off. We have little certainty over the actual thickness of the spacer between the nanocube and the mirror. Qualitatively comparing these results with our COMSOL simulations we can speculate that there is probably a spacer of under 5 nm thickness below the cube since the resonance is redder in experiments than in our simulations. This has been previously observed by T. Hoang in 2015 [33] also in the context of nanocubes over a thin polymer layer. Part of the spacer layer is the 3 nm protective PVP surrounding the cube. Gold roughness and other features can change the spacer thickness. We conclude that the dark field scattering spectra are in qualitative agreement with our COMSOL simulations.
(a)
(b)
Figure 22: Beautiful colours scattered by gold nanocubes in darkfield microscopy. Images were taken with a 8 megapixel smartphone camera through the optical path. Colours may be subject to slight automatic saturation. This is a qualitative observation.
5.2
Confocal fluorescence microscopy
In this section we show photoluminescence spectra of Coumarin 153 and Rho-damine 6G molecules confined under the nanocube after the O2 descum procedure.
This method can be used to quantify the emission enhancement as a consequence of the calculated LDOS enhancement [59] [25].
In figure 23 we show photoluminescence spectra from two different dye molecules embedded in thin PMMA pedestal under the nanocubes. These spectra were taken with a Nikon 20x 0.4NA (CF IC Epi Plan DI) objective. This objective was cho-sen because of its close resemblance to the objective employed in the cavity setup. Higher counts on the spectrometer (at same integration time of 1 s) were achieved by using a Nikon Plan Fluor 100x 0.9NA objective. Coumarin 153 has its emission peak in ethanol at 530 nm while Rhodamine 6G molecules at 550 nm. The pump light employed was a PicoQuant (LDH-P-450) 450 nm pulsed laser. A short pass filter (FESH0500, Thorlabs) is placed between the laser and the sample to remove unwanted wavelengths from the beam. In order to collect photoluminescence light
(a) PL from Rh6G. (b) PL from Cou 153.
Figure 23: Photoluminescence from dye molecules in the nanogap.
below 500 nm is filtered by part of two dichroic mirrors mounted within the mi-croscope turret: DCLP500 + ET460LP and HQ500LP. These emission peaks can be observed in the graphs in figure 23. On the red side of the Rh6G emission peak we find a further shoulder in PL. This could be attributed to PL from the PMMA matrix, which peaks at around 700 nm, as found in this work [51]. This work finds long wavelength emission from PMMA at 633 nm [54]. It is however peculiar that this signature does not show in the Coumarin 153 spectrum since both organic dyes are embedded within the same organic polymer. Furthermore, due to low quantity of the emitters in the film it was not possible to quantify photoluminescence enhancement due to the nanocube. As a matter of fact we re-port here the measured spectra without reference signal, since we used the plasma etching technique to remove all film from not under the cubes.
In figure 24 we report the camera images for a gold mirror with a 20 nm PMMA film doped with Rhodamine 6G molecules. These images were produced with a Nikon 20x 0.4NA (CF IC Epi Plan DI) objective and imaged on a PCO panda4.2 sCMOS 6.5 micron camera. It is not possible to see nanocubes (as dark spots) under white light illumination with the 20x objective. It is however possible to see them as dark spots with the 100x aforementioned objective. We firstly studied the emission from the dye molecules confined to a pedestal beneath the cube with the higher magnification objective. It could be concluded that the dark spots on the camera were nanocubes by comparing dark field microscopy images, images captured under white light and in photoluminescence. We could
(a) Laser light, PL on camera.
(b) White light illumination.
Figure 24: Photoluminescence from Rh6G molecules with a Nikon 20x 0.4NA (CF IC Epi Plan DI) objective.
find, in that order: colourful signatures and doughnuts, black spots and bright spots. We ensured we were looking at the same portion of the sample. It was especially easy to switch between white light and photoluminescence to verify the above claim while it required using markers such as dirt or scratches in order to map the surface morphology of the sample in dark field microscopy.
5.3
Nanoparticle enhanced scattering of nonlinear
emis-sion
In this section we use the architecture of the sample we designed for cavity experiments and the flexibility of the manufacturing method to measure two-photon absorption/emission in Rhodamine 6G (Rh6G) molecules. The sample is a transparent glass slide with a PMMA film spun on top. Embedded in the film are Rhodamine 6G molecules. In figure 25 we show light that was emitted by Rh6G molecules, and hotspots around nanocubes are visible. Rh6G molecules are pumped with a 16W IR 1030 nm pump PHAROS laser. All emission light that is outside the 500 nm to 650 nm range is filtered out with Thorlabs FESH0650 + Chroma HQ500LP filters, while the excitation light is filtered with Thorlabs FELH0700 and FESH0950. Emission is then focused on the camera. The
diffrac-tion limited bright spots are the regions of enhanced scattering of the emission. This process shows that Rhodamine 6G molecules absorb two photons at IR wave-length and then emit in the 550 nm range because the only pump light available to them is above 950 nm. Keeping only light in the 500-650 nm range, we col-lect emission on the camera. This measurement hints that there could be field enhancement by part of the nanocubes at the pump frequency and perhaps an LDOS enhancement. In order to probe LDOS enhancement by part of this system either power or time resolved measurements could yield further insights.
Figure 25: Enhanced scattering of nonlinear emission of Rh6G molecules by nanocubes.
5.4
Nanoparticle enhanced Raman of Coumarin 153
We measure the Raman signal of Coumarin 153 molecules confined to the PMMA pedestal under the nanocube, using a 768 nm laser at 1mW and exposing for 200 ms. The sample is a 40 nm thick planar gold mirror with a thin 10 nm PMMA film with Coumarin 153 molecules embedded within. There was no control measurement on PMMA only films, thus we are not able to discern what signal could be coming from those molecules instead of Coumarin 153. Nanocubes are identified upon white light illumination as doughnut-like grey shadows on the sample. Once the laser is focused on the spot we record a measurement scan. When not on a nanocube the Raman signal is zero. The full measurement is reported in figure 26 and a time slice is reported in figure 27.
Figure 26: Raman spectrum of Coumarin 153 molecules in the nanogap as a function of time. The colour scale represents counts on our detector. The light used is a 768 nm laser. We integrate for 200 ms.
We take a slice at 19.6 s of the full time trace measurement. This is shown in figure 27. We can identify Stokes peaks. This slice was selected as it was the highest in counts out of the full trace measurement. This could be a Raman flare.
Flares are sudden peaks in background signal, due to the rearrangement of the gold atoms [12]. Another reason for this peak in counts could be the fact that the laser is close to the resonance with the gap mode between the mirror and the nanocube. The same data is shown as a function of wavelength, and as a function of energy shift in cm−1 relative to the pump wavelength. Plotting the Raman shift is conventional in vibrational spectroscopy, as the shift is independent of the pump wavelength, and given by the vibrational modes of the molecule in question. The flat part of the spectrum around 0 cm−1 is due to the filtering of the laser which is at 768 nm. By using incident light as a reference, it is possible to extract an absolute value for molecular vibration frequency.
Comparing this signal to the one reported by Y.Jiang et al in 1994 [38] we find some similarities. The signal we measure shows a peak at just below 500 cm−1. In the aforementioned source, Jiang et al report a peak at 456 cm−1. Another feature that is in qualitative common between the two signals is the large peak just below 1000 cm−1, in our measurement. J.Yiang et al reports a similar feature at 1155 cm−1.
In figure 27, to the left of the filtered light, we can identify anti-Stokes peaks. In a recent article, pico cavities have shown to produce high anti-Stokes peaks. Pico cavities can strongly enhance optical field gradients thus potentially exciting usually inactive Raman lines [18].
Figure 27: Raman signal of Coumarin 153 molecules from the full time trace. Sliced at 19.6 s.
6
Conclusion and outlook
We have theoretically investigated the behavior of a nanocube plasmonic antenna with a planar Fabry-P´erot cavity, designed and manufactured a sample, measured dark field scattering spectra, nonlinear emission and Raman of dye molecules.
We have shown simulation results which depict the cavity - antenna hybrid systems as an LDOS enhancing environment which outperforms both the cavity and the antenna when alone. The principal benefit of the hybridization is the gain in quality factor from the cavity and reduction in mode volume thanks to the plasmonic antenna. In our simulations this benefit occurs only when the cavity is blue detuned with respect to the plasmonic resonance of the antenna. While underlying mechanisms behind this effect are still unknown, a curved-planar mirror geometry for the cavity could further enhance the effect.
Experimentally we constructed a procedure to successfully and repeatably make a sample for the cavity experiment. With that sample we carried out characteriza-tion of the luminescence of the dye molecules we used. We measured a nanocube enhanced Raman signal from the dye molecules and nanocube enhanced scattering of nonlinear emission of fluorescent molecules.
These results show that this system is promising in reaching strong coupling between a planar cavity and a nanocube, to then include an emitter in the sys-tem. This system can be used to study strong coupling with different geometries of cavities both in simulations and in experiments, eventually with single pho-ton sources among other emitters. In experiments we found the biggest hurdle was maintaining bright emitters after descumming processes. This improves with higher fluorescent molecule concentration and with dyes with a higher quantum yield. Further research is needed in the struggle to reach brighter emitters and better tracking of the nanocubes on the mirror.
Taking a step back and considering simulation and experimental results as a whole, we ultimately conclude that the Fabry-P´erot-nanocube hybrid resonator holds the potential for monster LDOS enhancements, with direct implications in the strive for room temperature cavity QED, high fidelty single photon sources for quantum computing and sensor and detector technology.
7
Acknowledgements
First and foremost I’d like to thank my supervisor Femius for accepting me as a master student, for his passion for physics and for his patience. It was most inspiring to learn to think as a scientist from you and it was really admirable from my perspective to see how much work you put into actually being there for everyone that needs you, and many many people seem to need you all the time. Isabelle: thank you for teaching me COMSOL and helping me improve with Python. These are truly unique skills that I had the luxury to learn from you (also thank you for a million other things, but you know them already and they won’t fit in here). Next, I want to thank K`evin for all the physics talk. It was such a pleasure to share with you a love for science and an insatiable interest for all of physics, not just AMOLF physics. We often found each other to agree in our ideas, be it the club-med culture (as the Dutch and Germans decided to brand our Mediterranean countries in the midst of the corona-crisis), be it good affinity, it was great. Then Ilan, also thank you for the physics. And Tom also for the physics, for the jokes about the a daggers and the rest of the theory that I eventually managed to pass, perhaps thanks to those jokes too. I want to thank you Annemarie for the human being you are: your empathy, independence, brilliance and hard working ethic helped me grow up and will be a reference for some time to come. I want to thank the whole Resonant Nanophotonics for the support, knowledge and patience. I want to thank the other affiliated research groups for the insightful discussions and at times for borrowing a dark field microscope. Marko, you’re a straightforward guy I think: thank you. Ultimately, I want to wholeheartedly thank the NanoLab staff but especially Bob. You Bob are incredibly knowledgeable and your understanding is true, not pointlessly notional. Also not sure if you’ll read this, but Tomas in you I found a fellow mariner and a friend. I’m set on winning a nighttime wedstrijd on Extress someday. Finally, I want to thank AMOLF as a whole, the staff and the rest of the technical support group for all the great work which we all scientifically thrive upon.
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